A hydrodynamic model for chemo-mechanics of poroelastic materials

Abstract

Chemical dissolution along interfaces between solid skeleton and pore fluids tends to alter geomaterials and may cause catastrophic failures. Following the hydrodynamic procedure, this work develops a mathematically rigorous and thermodynamically consistent modelling framework to investigate the impact of chemo-mechanical coupling on the constitutive properties of poroelastic geomaterials. The formulation considers the mass fractions of all the ionic species in the pore fluid as independent state variables that quantify chemical processes. The constitutive and transport relationships are systematically derived from thermodynamic principles, symmetry requirements and conservation laws. To demonstrate its effectiveness, the formulation is adopted to study the dissolution process of saturated calcarenites under acidic environments. Simple density-dependent linear elasticity is being considered whereby stiffness degradation is physically captured in terms of density changes. Without chemical reaction, the stiffness is fixed and the response is purely linearly ‘poroelastic’. However, upon reaction the density changes, and thus so also does the stiffness, implying a non-linear response. The model also reveals the connection of densities to chemical potentials and pore fluid pressure, and shows that the latter quantity is governed by both density and osmotic concentration. Simulations of long-term debonding tests of calcarenite samples show good agreement with experimental observations under both uncoupled and coupled testing conditions. Furthermore, considering only a limited number of clearly stated assumptions, the model recovers the form of several empirical laws such as Darcy's law, Fick's law and the law of reaction kinetics. Outside these idealised model assumptions, the newly derived relationships generalise results for field conditions and provide insights into cases where one normally does not have, or technologically cannot reliably obtain experimental data due to challenging loading and boundary conditions.